Map dependence of the fractal dimension deduced from iterations of circle maps

Alstrøm, P.
Springer
Published 1986
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Physics
Notes:
Abstract Every orientation preserving circle mapg with inflection points, including the maps proposed to describe the transition to chaos in phase-locking systems, gives occasion for a canonical fractal dimensionD, namely that of the associated set of μ for whichf μ=μ+g has irrational rotation number. We discuss how this dimension depends on the orderr of the inflection points. In particular, in the smooth case we find numerically thatD(r)=D(r −1)=r −1/8.
Type of Medium:
Electronic Resource
URL: